Find the center of mass of a thin plate of constant density covering the given region.The region bounded by the parabola y = 36 - x2 and the x-axis

A.  = 0,  = 
B.  = 0,  = 
C.  =  = 0
D.  = 0,  = 


Answer: D

Mathematics

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Find the flux of the curl of field F through the shell S.F = -3yi + 9zj + 6xk; S: r(r, ?) = r cos ?i + r sin ?j + (4 - r2)k, 0 ? r ? 2 and 0 ? ? ? 2?

A. 6? B. 12 C. 12? D. -12?

Mathematics

Express the given function as a composite of functions f and g such that y = f(g(x)).y = (4x + 3)7

A. f(x) = 4x + 3, g(x) = x7 B. f(x) = x7, g(x) = 4x + 3 C. f(x) = (4x)7, g(x) = 3 D. f(x) = 4x7, g(x) = x + 3

Mathematics

Solve the differential equation.x2  = 8y

A. y = Ce- 8/x
B. y = -  + C
C. y = Ce- 8x
D. y = Ce8/x

Mathematics

Write the quotients with positive exponents.

A.
B. 5mp 
C.
D. 5m5p2

Mathematics